Research On The Distributed Formation Control And Optimization Of Multi-agent System

With the development of science,the working environment and task requirements have become more and more complex.Because the function of single agent is so simple,it is often powerless in many complex environments.So,inspired by the cooperation in nature.cooperative control between multiple agents has gradually attracted more and more scholars.As one of the methods in cooperative control,distributed control of multi-agnet system has the advantages of small computing capacity and high system fault tolerance.It mainly includes the following types of problems: clustering problem,formation problem,target estimation problem and optimization problem.Among them,the problem of distributed formation and optimization control is one of the hotspots in recent years.However,the existing literature mainly studies the dynamic model in an integral form,and in the optimization problem,the optimized performance index is often in the form a sum of the state function of system,not the functional form.Aiming at these defects,this paper studies and solves the flocking,formation and evolution of multi-agents based on the analysis of dynamic models of the agents.For the second-order continuous systems and discrete systems with internal coupling and the first-order discrete systems without coupling,the distributed optimal control problem is solved respectively.The main work and research results of this paper are listed as follows:1.Based on the dynamic analysis of wheeled robots,we design a distributed consensus protocol for the formation control problem and evolution problem of the first-order discrete multi-agent system.besides,we propose an evolutionary method to minimize the energy of the multi-agent system under condition that all the original communication channel have no changes.Then we design a distributed formation controller for second-order multi-agent system with considering the actual dynamic model,which can make the system reach the consistency in position,velocity and posture angle in any initial state.2.For at the distributed optimal control problem of first-order continuous-time and first-order discrete-time multi-agent systems with internal coupling.When the cost function is a quadratic form,a distributed optimization controller which only relies on the original internal coupling information and does not add any other communication is designed to finish te optimization control.It is to say,the coupling matrix of the controller has the same zero elements as the internal coupling matrix of the original system.At the same time,we add two controlled variables,self-coupling coefficient and mutual-coupling coefficient,to broaden the conditions for the existence of the optimal controller.Finally,the convergence of the system after adding the optimal controller is proved by simulation.3.Then,we study the distributed optimal control of second-order continuous system and second-order discrete system with integral performance index,meanwhile,we give sufficient conditions to ensure the integral quadratic performance index positive definite.Under these conditions,we use the thought of optimal control to design a distributed optimal controller,which can make the system to achieve consistency,and the performance index is the smallest.The analytical relationship between the coupling coefficient in the controller and the parameters in the performance index is also given at last.